MAT135COS Into to Statistics: MA1 SP17 (Brian Clark Homework: Chapter 3 Homework
ID: 3206353 • Letter: M
Question
MAT135COS Into to Statistics: MA1 SP17 (Brian Clark Homework: Chapter 3 Homework Score: 02 of 1 pts 17 of 31 (7 complete HW Score 3.2.31 The weight of organ has abel haped dw buton with a mean of 340 About 9% wil be between grams Uue the empirical to determine the following (bl What percentage between 310 grams and 3h0 grams? percentage organs than 310o than 370 grams? of weigh between 280 and 430 grams? lal and 400 68 Type an integer or a Question is complete Tap on the red indicators to see inowectanswers All parts showing E O Search right here A &Explanation / Answer
a) P(x) = P(z = (x-M)/sd)
P(z = (x1-340)/30) = 0.975
(x1-340)/30) = 1.96
x1 = 398.8
(x2-340)/30) = -1.96
x2 = 281.2
95% of the weights are between 281.2 and 398.8
b) Mean M = 340
standard deviation sd = 30
P(weight between 310 and 370 grams) = P(x=370)-P(x=310)
P(x) = P(z = (x-M)/sd)
so,
P(weight between 310 and 370 grams) = P(z= (370-340)/30) - P(z= (310-340)/30)
=P(z= 1) - P(z=-1)
= 0.8413 - 0.1587 {By using standard normal distribution table}
= 0.6826= 68.26%
c) P(x < 310g) = 0.1587
P(x>370g) = 1-0.8413 = 0.1587
P(weights less than 310g and more than 370g) = 0.1587+0.1587 = 0.3174 = 31.74%
d) P(weight between 280 and 430 grams) = P(x=430)-P(x=280)
P(x) = P(z = (x-M)/sd)
so,
P(weight between 280 and 430 grams) = P(z= (430-340)/30) - P(z= (280-340)/30)
=P(z=3) - P(z=-2)
= 0.9987-0.0228 {By using standard normal distribution table}
= 0.9759 = 97.59%
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